Molecular Biology of the CellVol. 21, 323–333, January 15, 2010

Fast Microtubule Dynamics in Meiotic Spindles Measuredby Single Molecule Imaging: Evidence That the SpindleEnvironment Does Not Stabilize MicrotubulesDaniel J. Needleman,* Aaron Groen,† Ryoma Ohi,† Tom Maresca,‡ Leonid Mirny,§and Tim Mitchison†

*School of Engineering and Applied Sciences, Molecular and Cellular Biology, Harvard University,Cambridge, MA 02138; †Systems Biology, Harvard Medical School, Boston, MA 02445; ‡Department ofBiology, University of North Carolina at Chapel Hill, Chapel Hill, NC 27599; and §Harvard-MIT Division ofHealth Sciences and Technology, and Physics, Massachusetts Institute of Technology, Cambridge, MA 02139

Submitted September 23, 2009; Revised November 10, 2009; Accepted November 17, 2009Monitoring Editor: Kerry S. Bloom

Metaphase spindles are steady-state ensembles of microtubules that turn over rapidly and slide poleward in somesystems. Since the discovery of dynamic instability in the mid-1980s, models for spindle morphogenesis have proposedthat microtubules are stabilized by the spindle environment. We used single molecule imaging to measure tubulinturnover in spindles, and nonspindle assemblies, in Xenopus laevis egg extracts. We observed many events where tubulinmolecules spend only a few seconds in polymer and thus are difficult to reconcile with standard models of polymerizationdynamics. Our data can be quantitatively explained by a simple, phenomenological model—with only one adjustableparameter—in which the growing and shrinking of microtubule ends is approximated as a biased random walk.Microtubule turnover kinetics did not vary with position in the spindle and were the same in spindles and nonspindleensembles nucleated by Tetrahymena pellicles. These results argue that the high density of microtubules in spindlescompared with bulk cytoplasm is caused by local enhancement of nucleation and not by local stabilization. It follows thatthe key to understanding spindle morphogenesis will be to elucidate how nucleation is spatially controlled.

INTRODUCTION

Mitotic and meiotic spindles are highly dynamic, self-orga-nizing ensembles of microtubules and interacting proteins.A fundamental aspect of spindle assembly is that the con-centration of microtubules is higher within the spindle thanelsewhere in the mitotic cytoplasm. This is particularly evi-dent for meiotic spindles that largely lack astral microtu-bules, including spindles assembled in Xenopus laevis eggextracts that we use in this study. From biochemistry (Changet al., 2004) and electron microscopy (EM) (Coughlin andMitchison, unpublished), we estimate the concentration ofpolymerized tubulin inside extract spindles is �60 �M,whereas outside spindles it is too small to measure, andcertainly �1 �M. A similar concentration gradient is evidentin vivo from images of unfertilized eggs (Wuhr et al., 2007).It is currently unclear what accounts for this strong concen-tration gradient. In principle, it could have several causes,including 1) local nucleation of microtubules in the spindle,2) global nucleation of microtubules and local stabilizationin the spindle, 3) global nucleation of microtubules followedby their translocation into the spindle by motors, and 4) localconcentration of soluble tubulin dimers within the spindlefollowed by their polymerization. In the egg extract system,

possibilities 3 and 4 have been largely ruled out by liveimaging of spindle assembly reactions (Groen et al., 2009),although we cannot exclude the possibility that some mod-ified form of tubulin dimer concentrates inside spindles.Local nucleation within spindles is perhaps the most intui-tive model, but the mechanism and rate of nucleation inanastral meiotic spindles is currently unclear. Local stabili-zation is also plausible. Since the discovery of dynamicinstability in the mid-1980s, models for spindle morphogen-esis have proposed that microtubules are stabilized by thespindle environment (Kirschner and Mitchison, 1986; Karsentiand Vernos, 2001).

The issue of microtubule stability in spindles is compli-cated by the fact that they contain multiple microtubulepopulations whose nucleation and stabilization mechanismsmay differ. Kinetochore, astral, and nonkinetochore micro-tubules population have been distinguished by structuralcriteria, and it is possible that other subpopulations exist.Kinetochore microtubules are known to be strongly stabi-lized in most systems, presumably because kinetochore pro-teins prevent rapid depolymerization of their plus ends(reviewed in Inoue and Salmon, 1995). Egg meiotic spindlescontain few astral microtubules, and we do not discuss themfurther. Nonkinetochore microtubules are by far the mostabundant class in egg meiotic spindles (e.g., see EM views inMitchison et al., 2004) and also the most abundant class inmammalian somatic spindles in anaphase (Mastronarde etal., 1993). They have been much less studied than othermicrotubule classes, yet they are responsible for morphol-ogy, bipolarity, and size in egg extract spindles and proba-bly in anastral spindles more generally. We know this be-

This article was published online ahead of print in MBC in Press(http://www.molbiolcell.org/cgi/doi/10.1091/mbc.E09–09–0816)on November 25, 2009.

Address correspondence to: Daniel J. Needleman (dan_needleman@harvard.edu).

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cause spindles with normal morphology, but lackingkinetochores and centrosomes, assemble around DNA-coated beads in egg extracts (Heald et al., 1996). Thus, if weunderstood how the nonkinetochore population is nucle-ated, spatially organized, and (perhaps) stabilized, wewould understand the essence of meiotic spindle morpho-genesis, and probably important aspects of the mitotic prob-lem.

The organization and dynamics of nonkinetochore mi-crotubules are poorly understood. In the extract system,their assembly is promoted by Ran-guanosine triphosphate(GTP) and Aurora-B kinase activity that have been proposedto instruct spindle morphogenesis (Karsenti and Vernos,2001; Sampath et al., 2004; Maresca et al., 2009). These factorshave the potential to promote both nucleation and stabiliza-tion of microtubules, by desequestering spindle assemblyfactors in the case of Ran-GTP (Caudron et al., 2005), and byinhibiting microtubule-destabilizing proteins in the case ofAurora-B (Ohi et al., 2004). However, the extent to whichthese gradients are truly responsible for morphogenesis, andthe extent to which they promote nucleation versus stabili-zation, is unclear. Evidence that soluble gradients from chro-matin promote stabilization on nonkinetochore microtu-bules has come from experiments where the growth ofsingle microtubules toward versus away from chromatinmasses was imaged (Athale et al., 2008). Although thesereconstitution experiments allow single microtubule imag-ing, they may not accurately model the environment in thecenter of the spindle. Thus, there is a need to directly mea-sure the stability of nonkinetochore microtubules insidespindles and to compare them with microtubules with freeplus ends assembled outside spindles.

Direct observation of single microtubules in spindles iscurrently not possible because they are too close together tooptically resolve, so a variety of bulk methods have beenused to infer their dynamic behavior. Response to perturba-tion (Inoue and Sato, 1967) and fluorescence recovery afterphotobleaching (FRAP) (Inoue and Sato, 1967; Salmon et al.,1984) revealed that most spindle microtubules exchangewith the soluble monomer pool on a time scale of tens ofseconds. In addition, photomarking and speckle microscopyrevealed that both kinetochore and nonkinetochore micro-tubules slide continuously toward the poles (Sawin andMitchison, 1991; Valloton et al., 2003). All these data referprimarily to nonkinetochore microtubules, because theycomprise the bulk population inside the spindles used inthese studies. The data left unclear the detailed mechanismby which nonkinetochore microtubules turnover. Dynamicinstability of plus ends has long been a plausible candidate(Sawin and Mitchison, 1991; Inoue and Salmon, 1995). How-ever, many published models implicate depolymerizationfrom minus ends as the major turnover mechanism, oftenproposing depolymerization by a combination of motor-driven sliding toward pole with depolymerase activity atminus ends, a class of model we refer to as “feeder-chipper”models (Gadde and Heald, 2004). One reason our under-standing of turnover mechanism is limited is that bulkmethods—perturbation, FRAP and photoactivation—are prob-lematic for accurately measuring dynamics, particularly atshort time scales in which monomer diffusion and polymer-ization dynamics both contribute to recovery kinetics. Thus,recovery kinetics in a FRAP experiment are sensitive toexperimental details that are difficult to quantitatively ac-count for, such as the exact three-dimensional shape of thebleached region (Axelrod et al., 1976), the method of normal-ization, and the specifics of the bleaching protocol (Weiss,2004). Factors such as local reincorporation of bleached

monomer can results in estimates of recovery times that candeviate from their true value by a factor of �3. Even if thesesystematic errors are accurately corrected, FRAP recoverytime scales of binding may not directly relate to reactionrates (Beaudouin et al., 2006), implying that FRAP of fluo-rescently labeled tubulin in spindles might not unambigu-ously determine microtubule lifetimes. For example, the rateof turnover of a marked region can depend on its distancefrom microtubule plus ends and the extent to which releasedtubulin becomes reincorporated into other microtubules inthe spindle. These considerations complicate interpretationof FRAP data that have suggested different turnover rates atthe middle of spindles versus near poles (Pearson et al., 2006;Cheerambathur et al., 2007). Speckle microcopy provides adifferent approach to measuring turnover. Labeling approx-imately one tubulin molecule in 1000 generates a stochastic,inhomogeneous distribution of fluorescence, whose brighterregions are called “speckles.” Speckle dynamics has pro-vided important insight into motion and turnover in cy-toskeletal ensembles (Danuser and Waterman-Storer, 2006).However, one speckle corresponds to multiple flurophores,presumably incorporated into multiple microtubules, so it isdifficult to directly relate speckle turnover to individualfilament turnover. Taken together, published dynamicsmeasurements have not fully answered the questions ofwhether the spindle environment stabilizes microtubulesand whether microtubule turnover is spatially regulated inspindles nor have they elucidated the kinetic mechanism ofmicrotubule turnover.

In this study, we analyze the statistics of immobilizationof single molecules of tubulin in spindles, which we showreports on assembly and disassembly of subunits into mi-crotubules. This approach depends on the fact that a tubulinmolecule in a microtubule moves slowly and thus appears asa point on the camera, whereas a soluble subunit diffusesrapidly compared with our image acquisition speed andtherefore blurs out. Our method is a form of speckle micros-copy, although a key difference is that we image the dynam-ics of individual tubulin molecules, so we can more directlyinfer the dynamics of individual microtubules. Single mol-ecule methods allow time distributions of individual molec-ular events to be measured in situ, which, when combinedwith mathematical modeling, can be used to extract quanti-tative information that is difficult to obtain with bulk tech-niques (Sako, 2006). We find this is indeed the case for singletubulin imaging in spindles; our results answer the questionof whether microtubules are stabilized in spindles and re-veal fundamental aspects of the turnover mechanism. Wefocus on tubulin turnover and its implications. Our resultsare thus complementary to a recent study that analyzedmovements of single tubulin molecules in X. laevus eggextract spindles but did not address turnover (Yang et al.,2007).

EXPERIMENTAL PROCEDURES

Preparation of X. laevis Extract SamplesSpindles were assembled in X. laevis egg extracts, after DNA replication, asdescribed previously (Sawin and Mitchison, 1991). Typically, 4–6 �l of spin-dle reaction was squashed under 18-mm coverslips. Only one spindle wasimaged per coverslip, and spindles that changed morphology or underwentsubstantial motion during imaging were discarded. For each condition, singlemolecule experiments were performed on 3 to 10 spindles per extract prep-aration, which was repeated on three to five different extracts prepared ondifferent days. In total, thousands to tens of thousands of molecules wereanalyzed for each condition.

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Reagents2-(1-(4-Fluorophenyl)cyclopropyl)-4-(pyridin-4-yl)thiazole (FCPT) was syn-thesized as described previously (Groen et al., 2008) and stored as a 200 mMstock in dimethyl sulfoxide. The FCPT stock was further diluted to 20 mM inextract and added to preformed spindles to a final concentration of 200 �M.Movies were acquired rapidly after drug addition. Mitotic centromere-asso-ciated kinesin (MCAK) was immune depleted from extract, and purifiedbaculovirus-expressed MCAK was added back to various levels as describedpreviously (Ohi et al., 2007). Tetrahymena pellicles were purified following theprotocol of Coue et al. (1991).

Single Molecule ImagingTubulin was directly labeled with Alexa-647, by using the protocol of Hymanet al. (1991), and added to a final concentration of �150 pM, such that of orderone in 100,000 tubulin molecules were labeled. Using an infrared dye resultedin enhanced signal to noise compared with fluorophores that emit visiblelight, due to minimized image degradation by background autofluorescence(data not shown). Data were acquired on a microscope (model E800; Nikon,Tokyo, Japan), with 60� or 100� objectives (1.4 numerical aperture Plan Apodifferential interference contrast; Nikon), a spinning disk confocal (CSU-10;Yokogawa, Newnan, GA), and a backilluminated electron multiplying (EM)charge-coupled device (CCD) camera (iXonEM � 897 or iXonEM 860; AndorTechnology, Belfast, Northern Ireland), with maximal EM gain. Movies weretaken with streaming acquisition using the SOLIS software package (AndorTechnology). Each image consisted of averaging 16 separate 100-ms expo-sures, which reduces the noise resulting from the stochastic gain process.Illumination was provided by the 647 line of an argon-krypton mixed gaslaser, with a total power of �3 mW after the microscope objective, corre-sponding to only 0.1–0.5 kW/cm2. Images were acquired 3–10 �m from thecoverslip as a balance between minimize potentially perturbing effects of theboundary while maintaining high signal to noise, which rapidly degradeswith depth of focus.

Particle TrackingImages of single molecules were of high enough quality that the position ofeach molecule could be tracked using freely available MATLAB code developedfor colloidal physics (Crocker and Grier, 1996) (http://www.seas.harvard.edu/projects/weitzlab/matlab/). In this particle tracking method (Crocker andGrier, 1996; Figure 1), raw images are background corrected with a boxcaraverage, convolved with a Gaussian kernel to suppress high-frequency noise,and local maxima of the filtered image above a threshold brightness areselected as candidate particles. For tracking displacements, the subpixel lo-cation of molecules was determined by fitting the intensity around eachparticle to a two-dimensional Gaussian (Thompson et al., 2002; Figure 1A), butthe pixel location of particles is sufficient for the measurement of tubulinlifetimes, and subpixel refinement was not used in that analysis. Particle

locations were linked to trajectories by a global minimization of the sum of thesquare of particle displacements between frames (Crocker and Grier, 1996).Additional analysis and data fitting were performed using custom writtenMATLAB code.

RESULTS

Single Molecule Imaging Can Be Used to InferPolymerization DynamicsMeiotic spindles with replicated chromatin were assembledin X. laevis egg extracts by standard methods (Desai et al.,1999). Spindles were labeled by assembly in the presence of�150 pM Alexa-647–labeled tubulin, such that approxi-mately one in 100,000 molecules were labeled. In some cases,the probe was added after assembly and allowed to incor-porate for �10 min with similar results. This wavelengthwas chosen because the probe has high molecular brightnessand very slow bleaching when deoxygenated (see below),and the autofluorescence background is lower in the infra-red, which greatly facilitates single molecule imaging. Spin-dles were identified by Hoechst staining of DNA and thenimaged in the 647 nm channel with a spinning disk confocalmicroscope and an EM-CCD camera. Images were collectedcontinuously every �2 s with no shuttering, by averaging�16 consecutive exposure that were collected from the cam-era every �100 ms. Images were collected from focal planescloser to the coverslip than most kinetochores, whichselected for signal from nonkinetochore microtubules andimproved image quality. These image sequences revealedwell-defined, discrete points of light emission scatteredthroughout the spindle (Figure 1, A and C, and Supplemen-tal Movie 1), which had Gaussian intensity profiles, andsignal-to-noise values between 4 and 10 (Figure 1). We es-tablished that these particles are single tubulin molecules byusing several criteria: They appeared and disappeared in astep-like manner during regular observation (Figure 1B andSupplemental Data); bleaching was negligible under ourstandard imaging conditions (see below), but when we pro-

Figure 1. (A) Raw images were filtered andsmoothed, and local maxima above a thresh-old brightness were selected as candidate par-ticles (Crocker and Grier, 1996). For trackingdisplacements, the subpixel location of mole-cules were determined by fitting the intensityaround each particle to a two-dimensionalGaussian, but the pixel location of particleswas sufficient for the measurement of tubulinlifetimes and subpixel refinement was notused in that analysis. (B, left) Particle loca-tions were linked to form trajectories by aglobal optimization procedure (Crocker andGrier, 1996). (B, right) Individual particles ap-peared and disappeared in a step-like man-ner. A particle’s lifetime is defined as the dif-ference between the times of disappearanceand appearance. (C) Raw image of a spindlewith single molecule level labeling.

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moted it by poisoning mitochondrial metabolism with aden-osine 5�-(�,�-imido)triphosphate) (AMPPNP), each particlesbleached in a single step-like manner and the populationbleached with single exponential kinetics (SupplementalData). It has also been argued previously, using intensitymeasurements, that with this level of labeling in extractspindles, �98% of particles imaged by widefield microscopywere single fluorophores (Yang et al., 2007).

Particles in the image report on the location of tubulinmolecules that are incorporated into spindles. Each frame inthe movies took �2 s to acquire, in which time freely dif-fusing tubulin would move micrometers, so fluorescencefrom soluble tubulin blurs over multiple pixels (Watanabeand Mitchison, 2002; Valloton et al., 2003; Kim et al., 2006).This is the same principle that underlies speckle microscopy(Waterman-Storer and Salmon, 1998), except that in our casethe signal comes from a single tubulin molecule and there-fore reports on the dynamics of a single microtubule. Stan-dard software from colloidal physics (Crocker and Grier,1996) was used to identify and track the particles (Figure 1).We tracked particles that existed for at least two frames toeliminate spurious identification, which was a highly con-servative approach as such misidentification events were notmanually observed, so our effective temporal resolution was�4 s. All the molecules underwent extensive motion, similarto that reported in a previous single molecule study (Yang etal., 2007). Motion was directed primarily toward the nearestspindle pole (Figure 2, left), as expected from previous pho-toactivation (Sawin and Mitchison, 1991) and speckle mi-croscopy (Valloton et al., 2003) observations. This motion isthought to reflect motor-driven sliding of individual micro-tubules within the spindle. Individual molecules displayed awide range of velocities, and frequent velocity changes, thatare not evident with averaging methods. Movement wasgenerally slower at the poles, consistent with previous re-ports (Burbank et al., 2007; Yang et al., 2008). Detailed anal-ysis of microtubule movements will be reported elsewhere.

In addition to moving, particles appeared and disap-peared in a step-like manner (Figure 1B and SupplementalMovie 1). Because soluble tubulin cannot be visualized inthese experiments, and incorporation into microtubules isthe only known way that tubulin molecules become immo-bilized in spindles, it is likely that particle appearance re-flects a tubulin molecule becoming incorporated into agrowing microtubule, and disappearance is caused by therelease of that molecule during microtubule depolymeriza-

tion. However, disappearance of fluorescent moleculescould also be caused by photobleaching or translocation outof the focal plane, and appearance could be caused by move-ment into the focal plane. The movement of the moleculerelative to the focal plane, if that occurs, could be artifactual(due to focus drift) or biological (due to microtubule move-ment). We therefore systematically investigated the extentwhich these nonturnover processes might contribute to par-ticle dynamics, and also the effect of perturbations that areknown to change microtubule polymerization dynamics.Summarizing in advance, all out data point to the majorityof particle appearance/disappearance faithfully reportingon microtubule assembly/disassembly events, and not otherprocesses.

Characterization of PhotobleachingWe first measured the number of observed tubulin mole-cules per spindle as a function of imaging time under ourstandard conditions and found they did not decrease overminutes of continuous observation (Supplemental Figure 1).This is consistent with a lack of bleaching, but the totalnumber of fluorescent tubulin molecules in the spindlecould also remain constant in the presence of photobleach-ing if the depletion of fluorophores is compensated by thediffusion and incorporation of new labeled tubulin into thespindle. To test the second possibility, we added two drugsthat together froze all microtubule dynamics in spindles.Taxol was added at high concentration to block polymeriza-tion dynamics, and the kinesin-5 inhibitor FCPT was addedto freeze microtubule motions. FCPT binds to kinesin-5 com-petitively with ATP, with high affinity and high specificityover a panel of eight kinesins and 38 kinases (Rickert et al.,2008). In the spindle, FCPT blocks kinesin-5 in a state withhigh affinity for the microtubule lattice, converting it into animmobile cross-linker (Groen et al., 2008). In the presence ofFCPT, essentially all measurable tubulin motion is blockedin spindles (Figure 2, right). More commonly used allostericinhibitors of kinesin-5, such as monastrol and S-trityl-cys-teine, prevent coherent microtubule sliding to the poles(Miyamoto et al., 2004) but do not stop all motions of tubulinmolecules (data not shown). Presumably, FCPT blocks mo-tion more completely than the allosteric kinesin-5 inhibitorsbecause FCPT not only prevents kinesin-5 motor activity butalso induces cross-linking. Even with microtubule polymer-ization dynamics and sliding movement both frozen, thenumber of observed fluorescent tubulin molecules per spin-dle did not decrease over several minutes of continuousimaging (Supplemental Figure 2), demonstrating that pho-tobleaching is truly negligible under our standard imagingconditions. Furthermore, under these conditions, many par-ticles could be tracked for �100 s, much longer than waspossible in untreated spindles, arguing that instrument driftin the z-axis is not responsible for particle appearance anddisappearance. Z-drift would have been unlikely even fromparticle behavior in standard image sequences, because in-dividual particles had a large range of lifetimes and ap-peared and disappeared in a step-like manner (see below),whereas Z-drift would cause gain and loss of signal in agradual, synchronous manner. We believe that the observedextraordinary photostability is due in part to efficient deple-tion of oxygen by the abundant mitochondria in egg extracts(Niethammer et al., 2008). Poisoning extract metabolism witha nonhydrolysable ATP analogue AMPPNP, allowed rapidphotobleaching, which we used to argue that the particlesare single molecules (discussed above and in SupplementalFigure 2).

Figure 2. Trajectories of particles in spindles are illustrated bydisplaying the dynamics of particles located in a particular frame. Aparticle’s future trajectory is colored red, its past trajectory is blue,and particles that were born in the selected frame are indicated bya green square. The shorter trajectories in the FCPT-treated spindleillustrate the reduced tubulin motion in this structure. Bar, 10 �m.

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Tubulin Turnover Dynamics in Spindles in the Absence ofTranslocationBecause photobleaching is not significant under our stan-dard imaging conditions, particle appearance and disap-pearance could be caused by assembly/disassembly or bymovement through the focal plane due to microtubule trans-location. To test which process dominates, and to simplifyparticle dynamics for initial analysis, we blocked microtu-bule motion in spindles by using FCPT, now in the absenceof Taxol. This inhibitor blocked all detectable particle move-ment in the spindle (Figure 2, right), with only slight resid-ual motion caused by small movements of the entire spindle.Despite this lack of motion, individual particles still ap-peared and disappeared in a step-like manner (Supplemen-tal Movie 2). A detailed analysis of the change in intensitiesof individual molecules showed that they appeared anddisappeared in a truly step-like manner, and not by thegradual change of intensity expected for a molecule movingthrough the focal plane (Supplemental Data). Thus, in thesehighly perturbed spindles, neither photobleaching normovements into and out of the focal plane are significant, soparticle appearance and disappearance can unambiguouslybe interpreted in terms of tubulin polymerization and depo-lymerization. Therefore, we were in a position to accuratelyquantify tubulin turnover in FCPT-treated spindles.

Observation of Fast Dynamics and Parameterization ofMicrotubule TurnoverWe refer to the total amount of time a tubulin molecule isimmobilized—the time between its appearance and disap-pearance in the image sequence—as its “lifetime” (Figure1B). The lifetime accounts for the times that tubulin is addedand removed from a microtubule; both events presumablyoccurring at microtubule ends. Thus, this data providesinformation that is somewhat different from a classic FRAPexperiment that measures the time of turnover of a markedregion inside microtubules, typically an unknown distancefrom the microtubule ends. We computed histograms oflifetimes from 13 different FCPT-treated spindles and foundthat they were similar, so we pooled the data (20,239 events)to construct a master curve that represents a histogram of allmeasured lifetimes (Figure 3). Almost 25% of the lifetimeswere in the shortest time bin of the histogram, correspond-ing to lifetimes of �4 s. These events correspond to very fastpolymer turnover that would be difficult to distinguish from

diffusion of soluble dimer into the bleach zone by FRAP. Thesignificance of these very fast events is discussed below.

We next sought to parameterize the entire lifetime distri-bution. It was manifestly nonexponential, as it is not astraight line on a linear-log plot (Figure 3). Thus, it cannot becharacterized solely by its half-time, and we sought alterna-tive, simple parameterizations that would allow quantitativecomparison of different conditions. In general, there is noreason to suspect that the distribution of lifetimes for sub-units in a dynamic polymer should be an exponential, or asum of exponentials, because the dissociation process is nota simple first-order reaction if exchange is limited to thepolymer ends. Rather, the distribution of subunit lifetimes isthe distribution of first passage times of the polymer’s ends,i.e., the time it takes the polymer end to return to the pointwhere the molecule was incorporated. In the simplest mod-els of polymer growth, the polymer length undergoes abiased random walk (Philips et al., 2009). The bias is ameasure of the tendency of the polymer to grow or shrink onaverage, whereas the randomness is caused by stochasticityin the polymerization process (see Supplemental Data). Avariety of more complex models of microtubule growth canbe approximated as a biased random walk in the appropri-ate limit (Hill, 1987; Bicout, 1997). Dynamics of single mi-crotubules in interphase cells (Vorobjev et al., 1997) andFRAP measurements of tubulin turnover (Maly, 2002) can bewell described by a biased random walk model, indicatingthat this approximation can apply to microtubules in vivo.

In a biased random walk approximation, the distributionof first passage times for a microtubule of length x to returnto length x after growing to some greater length—and hencethe predicted probability, P, of observing a tubulin moleculewith a lifetime of t when dissociation occurs at the same endas association—is given by:

P�t� � t3/2et� (1)

where � is four times the expected lifetime of a microtubuleof average length (Bicout, 1997; Supplemental Data). Figure3 (red line) shows a fit of this equation to the measuredlifetime distribution in FCPT-treated spindles. An excellentfit to Equation 1 is obtained with � 71 � 3 s. Thus, theentire lifetime distribution can be characterized with just asingle parameter, �. The lifetime data could also be fit to asum of two exponentials (data not shown), but such a fitinvolves two additional freely adjustable parameters (theamplitude and time constant of the second exponential),produces a fit of worse quality (the sum of residuals for the twoexponential best fit is 3.6 � 103, compared with 0.53 � 103 forthe biased random walk model), and we are unaware of anytheoretical justification for suspecting that the lifetime datashould be described as a sum of exponentials. We thereforeused fits to the biased random walk model to parameterizeour data. It is important to emphasize that this model is aphenomenological model that can at best be considered asan approximation to the true microscopic dynamics ofmicrotubules. Mechanistic implications of the excellent fitto a random walk model are considered in the discussionsection.

Tubulin Turnover Dynamics in Unperturbed SpindlesThe measurements of tubulin lifetimes described abovewere made on spindles in the presence of FCPT, whicheliminated potential artifacts caused by tubulin transloca-tion, but is a highly perturbing treatment that might modifymicrotubule polymerization. We therefore performed simi-lar measurements of tubulin lifetimes on unperturbed spin-

Figure 3. Distribution of tubulin lifetimes in spindles with FCPT(blue circles). A best fit to Equation 1 is included (red line, � 71 � 3s). The data and best fit were normalized to have an area of 1.

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dles. We pooled data from 27,478 single molecules from 13different spindles to construct the lifetime distribution. Al-though tubulin molecules in control spindles undergo ex-tensive motion, unlike in FCPT-treated spindles in which nodetectable translocation is observed (Figure 2 and Supple-mental Movies 1 and 2), the lifetime distribution for both setsof spindles was strikingly similar (Figure 4A). The similaritiesof the distribution of tubulin lifetimes in the absences of trans-location (with FCPT) and in the presence of translocation (con-trol) further argues that movement through the focal planedoes not contribute to the observed lifetimes.

A large fraction of fast turnover events were observed inunperturbed spindles, and again the entire lifetime distribu-tion was well fit by the biased random walk model. For theunperturbed spindles, a best fit to Equation 1 yields� 64 � 6 s and cannot be distinguished from the value of� 71 � 3 s obtained for FCPT-treated structures (P � 0.30,using a two-sample two-sided t test). Below, we show thesame is true even if only lifetimes �30 s are analyzed. Thisresult argues that kinesin-5 activity is not a major determi-nate of microtubule turnover dynamics in X. laevis egg ex-tract spindles, in contrast to what has recently been sug-gested in yeast spindles (Gardner et al., 2008). The yeast datapertained mainly to kinetochore microtubules, and it is pos-sible that kinesin-5 can alter kinetochore microtubule dy-namics indirectly, by influencing chromosome motion. Weconfirmed that FCPT does not strongly alter bulk tubulinturnover by a cruder, but more familiar measurement, of the

dynamics of incorporation of a pulse of fluorescently labeledtubulin into spindles. Spindles assembled in Alexa-488 tu-bulin, pretreated with FCPT or not, were mixed with extractcontaining XRhodamine tubulin and observed by live imag-ing. The time scale of incorporation of the red labeled tubu-lin was unaffected by FCPT (Supplemental Figure 4), con-firming the quantitative conclusion from single moleculeimaging. We conclude that neither kinesin-5 activity, normicrotubule sliding, are required for fast turnover of nonk-inetochore microtubules in X. laevis egg extract spindles.

Perturbing Microtubule Stability Alters Tubulin Lifetimesin the Expected MannerTo further test whether the distribution of single moleculetubulin lifetimes measures microtubule stability, and toquantify the effects of an important dynamics regulator, wechanged the concentration of MCAK (also called XKCM1), amicrotubule-depolymerizing kinesin-13 that is a major neg-ative regulator of polymerization in X. laevis egg extracts(Walczak et al., 1996). MCAK was immunodepleted fromextracts; pure, expressed MCAK (Ohi et al., 2007) was addedback to various concentrations; and spindles were assem-bled and studied with single tubulin imaging. Average life-times increased as MCAK concentration decreased; best fitsto Equation 1 resulted in � 97 � 11 s with 50% endogenousMCAK, � 61 � 5 s with 100% MCAK, and � 47 � 3 swith 200% MCAK (Figure 4B and Table 1). In the biasedrandom walk model, the expected lifetime of a microtubule of

average length is given by�

4 (Bicout, 1997), so we infer that

changing the concentration of MCAK causes a change in mi-crotubule stability. Spindle length also increased with decreasingconcentrations of MCAK (Ohi et al., 2007), as might be expected ifMCAK shortens microtubules. Thus, a molecule-specific pertur-bation known to effect microtubule polymerization dynamics ef-fects tubulin lifetimes in the expected manner, supporting ourconclusion that the tubulin lifetime distribution provide a quan-titative measure of microtubule stability in spindles.

Turnover Kinetics Are Spatially Uniform in SpindlesMany models have proposed that microtubule stability isspatially regulated in spindles. To critically test this, wedivided spindles into five equal subregions (Figure 5A) andseparately quantified dynamics in each region, pooling datafrom 13 unperturbed spindles. First, we measured the ratioof particle deaths to births in each region. This quantifieswhether there is a net bias toward assembly or disassembly.There were more total events in the middle of the spindle(data not shown), presumably because there are more plusends there (Burbank et al., 2006), but the ratio of deaths to

Figure 4. (A)Tubulin lifetimes are the same in unperturbed spin-dles (control, green symbols) and when microtubule translocation isblocked with FCPT (�FCPT, blue symbols). Best fits to Equation 1are displayed without FCPT (black line, � 64 � 6 s) and withFCPT (red line, � 71 � 3 s). (B) Increasing concentration of MCAK,a microtubule depolymerizer, results in decreasing tubulin life-times. Spindles were assembled in extract with MCAK reduced to50% native levels (green symbols and black line best fit to Equation1, � 97 � 11 s) or 200% native levels (blue symbols and red best fit,� 47 � 8 s).

Table 1. Table summarizing the measured microtubule stability, �, determined from fits to the tubulin lifetime distribution, and typicalmicrotubule sliding rate, obtained from a linear fit to the square root of the average mean-squared displacement of tubulin molecules, fordifferent conditions

Control � FCPT 200% MCAK 100% MCAK 50% MCAK

� (s) 64 � 6 71 � 3(0.30)

47 � 3(0.014)

61 � 5(0.70)

97 � 11(0.012)

Sliding rate(�m/min)

2.17 � 0.62 1.65 � 0.55(0.53)

2.14 � 0.28(0.96)

2.00 � 0.47(0.83)

The p values from a two-sample two-sided t test, testing whether the measurements are different from those obtained from control spindles,are recorded under each entry. Values that are significantly different from control spindles (p � 0.05) are in bold. Within the error of themeasurement, no motion is detected in FCPT-treated spindles (apart from small bulk movements of the entire structure).

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Molecular Biology of the Cell328

births was nearly equal to one at all positions (Figure 5B).There is a slight tendency toward more deaths at the polesand births at the center, but it is not clear whether this isstatistically significant. At steady state, there must be somepreference for birth near the spindles middle and deathsnear poles to balance microtubule sliding, but this effect isevidently very small. The majority of tubulin moleculesdisappeared in the same region they appeared in, reflectingour observation that turnover (measured as lifetimes) wasfast compared with sliding velocities. Approximately 75% oftubulin molecules disappeared in �20 s, and in this timethey only moved �0.5 �m, although there was large varia-tion between individual molecules in both velocity and life-time. This conclusion is consistent with results from earlyFRAP studies, which were incapable of measuring translo-cation in spindles because turnover was so fast (Salmonet al., 1984).

We measured the lifetime distribution in different subre-gions of spindles to investigate potential spatial variations inmicrotubule stability (Figure 5C). The three distributionswere indistinguishable, implying uniform lifetimes, andtherefore spatially uniform microtubule stability. This resultargues against the proposal that bulk microtubule stabilityincreases near chromosomes, as proposed in chromatin gra-dient models. Our observation that microtubule turnoverrate is the same at different positions in egg extract spindlesis supported by FRAP experiments (Supplemental Figure5A; Uteng et al., 2008).

Comparison of Tubulin Turnover Inside and OutsideSpindlesWe next tested whether microtubules are stabilized by thespindle environment. We did this in two ways, by compar-ing our lifetime data to literature observations of singlemicrotubule growing from centrosomes, far removed fromspindles, in X. laevis extracts, and by directly measuringsingle tubulin lifetimes in a nonspindle assembly. As de-

scribed above, our measured distribution of tubulin life-times in spindles can be accounted for by a very simplemodel of microtubule dynamics with just one freely adjust-able parameter, � (Figures 3 and 4). A best fit for unper-turbed spindles is obtained with � 64 � 6 s. In a phenom-enological model of microtubule dynamics as a biasedrandom walk, � is 4 times the expected lifetime of a micro-tubule of average length (Bicout, 1997). Our estimate formicrotubule lifetimes in spindles can be compared with theestimated average lifetime of single microtubules elongatingfrom centrosomes in mitotic egg extract, which was �20 s intwo published studies (Belmont et al., 1990; Verde et al.,

1992). The similarity of this value to�

4 (�16 s) suggests that

nonkinetochore microtubules in the spindle environmentare no more stable than microtubules nucleated from iso-lated centrosomes in mitotic egg extract. However, this ar-gument is based on comparing two different types of exper-imental measurements using the biased random walk modelto infer the half life of a microtubule from the single mole-cule tubulin lifetime, so it was also important to perform ahead-to-head comparison of spindle and nonspindle arraysindependent of any specific theory.

To directly compare microtubule stability inside and out-side of spindles, we performed a single molecule lifetimeanalysis on a nonspindle assembly. Our initial attemptsusing microtubules nucleated from centrosomes and axon-emes failed because the density of microtubules is too low inthese structures to obtain sufficient data to construct a life-time distribution. We therefore turned to Tetrahymena pel-licles, which contain hundreds of basal bodies, capable ofnucleating thousands of microtubules (Heidemann andMcIntosh, 1980; Coue et al., 1991). Pellicles incubated in X.laevis egg extract generated a dense array of microtubules ontheir surface (Figure 6A) that allowed measurement of singlemolecule lifetimes by the same protocol that was used forspindles. A lifetime distribution of tubulin molecules wascomputed from 7,362 events from nine pellicles. The result-ing distribution is visually indistinguishable from the one ob-tained from control spindles (Figure 6B), and a fit to Equation1 yields � 71 � 9 s, implying, within error (P �0.52, using atwo-sample two-sided t test), the same microtubule stabilityas measured in spindles (� 64 � 6 s). This result directly

Figure 5. (A) Spindles were divided into fifths; two pole regions(green), two midregions (blue), and one central region (red). Bar, 10�m. (B) Ratio of particle deaths to births is nearly equal to one in allregions. (C) Distributions of tubulin lifetimes in each region are thesame.

Figure 6. (A) Microtubules growing off of pellicles in X. laevis eggextracts. (A, top) Heavy labeling with Alexa-488 tubulin allows allmicrotubules to be visualized, but individual filaments cannot beresolved. (A, bottom) The same region as in A with single moleculelevel Alexa-647 tubulin. Bar, 10 �m. (B) Distributions of tubulinlifetimes from pellicles (pellicles, blue) and unperturbed spindles(control spindles, green) are very similar. Best fits to Equation 1 aredisplayed for pellicles (red, � 71 � 9 s) and spindles (black,� 64 � 6 s).

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demonstrates that nonkinetochore microtubules are not sta-bilized (or destabilized) by the spindle environment.

Analysis of Only Long-lived Tubulin MoleculesThe biased random walk model provides an excellent fit toour lifetime data (Figure 3). However, this cannot be takenas proof that this model is a literal description of microtu-bule dynamics. Rather, it is only phenomenological modelthat can quantitatively explain all of our data. Even thoughthe biased random walk model can explain all of our lifetimedata, covering �3 orders of magnitude of relative frequency(Figure 3), it is still possible that distinct portions of thelifetime curve are caused by mechanistically distinct pro-cess. For example, shorter lifetime events might correspondto rapid exchange of subunits within the GTP-tubulin cap(Howard and Hyman, 2009), whereas longer lifetimes mightcorrespond to the more global dynamics of length changesof the entire polymer. We therefore performed a furtheranalysis restricted to molecules with lifetimes �30 s. Forthese long times, both the biased random walk model and asingle exponential provide an excellent fit to the lifetimedata (Supplemental Figure 6), with R2 values �0.999. Expo-nential fits to lifetimes �30 s gives decay times of 22.0 � 0.7s for control spindles, 26.1 � 0.8 s for FCPT-treated spindles,and 23.3 � 1.6 s for pellicle-nucleated arrays of microtu-bules. Using these measures, data from the pellicle-nucle-ated arrays cannot be distinguished from control spindles(P � 0.45, using a two-sample two-sided t test). The FCPT-treated value is statistically significant difference from con-trol (p � 0.001, using a two-sample two-sided t test), but themagnitude of the effect is �10%. We again conclude that thespindle environment does not stabilize microtubules com-pared with pellicle-nucleated arrays and that kinesin-5 andmicrotubule sliding makes at most a small contribution toturnover mechanism for bulk nonkinetochore microtubules.

We also tested the possibility that there is a small popu-lation of more stable tubulin molecules, with a half-life of 10min, by fitting the lifetime data for control spindles, re-stricted to times �30 s, to a sum of two exponentials, oneexponential with a decay time of 10 min and the otherexponential with a freely adjustable decay (data not shown).Kinetochore microtubules have been suggested previouslyto have a half-life of �10 min (DeLuca et al., 2006). This twocomponent fit gave the fraction of the fast exponential decayas 99.98 � 0.28%, which makes the contribution of the 10-min decay indistinguishable from zero (P � 0.95). Thus ourdata does not provide evidence for the existence of a morestable subset of microtubules, but we cannot rule out thepossibility that such microtubules exist. As noted above,images were acquired close to the coverslip to improveimaging and minimize the contribution from kinetochoremicrotubules, so we cannot rule out the possibility that amore stable subset of microtubules exists at other locations.

DISCUSSION

In summary, we developed a new method to quantify theturnover of individual microtubules in spindles, accuratelyquantified spindle polymerization dynamics in the 4- to 20-stime scale for the first time and provided evidence thatnonkinetochore microtubules are not measurably stabilizedby proximity to chromosomes or by the spindle environ-ment. Our measurements and conclusions apply to nonkin-etochore microtubules, which comprise the majority in X.laevis egg extract spindles, and not to kinetochore microtu-bules, which are known to be preferentially stabilized in

many systems. Because only nonkinetochore microtubulesare required for extract spindle assembly (Heald et al., 1996),our data imply that anastral spindle assembly can occurwithout microtubule stabilization. This finding held whenwe analyzed all lifetimes (i.e., �4 s) and also when werestricted the analysis to lifetimes �30 s, to remove possiblecomplication from microtubule tip dynamics that do notcontribute to micrometer-scale growth and shrinkage. Mi-totic spindles in mammalian somatic cells can also assemblewithout kinetochore microtubules, although in this casetheir structure is abnormal, with lower microtubule densityand increased pole–pole distance (DeLuca et al., 2002), so itis not clear to what extent our conclusion holds for astral,somatic mitotic spindles. More generally, spindles from dif-ferent organisms—such as yeast, flies, humans, and frogs—are known to be different and results from one system mightnot extrapolate to other systems.

Our results contradict models proposing that microtu-bules are preferentially stabilized by the spindle environ-ment, and this stabilization is the driving force for spindleassembly (Kirschner and Mitchison, 1986; Karsenti and Ver-nos, 2001). However, we view them as consistent with mostdirect observations of dynamics in spindles. For example,the classic finding from FRAP that the majority of spindlemicrotubules turn over in tens of seconds (Salmon et al.,1984) hardly suggests that the spindle is a stabilizing envi-ronment. The widespread credence given to stabilizationmodels may reflect the fact that students of the spindle tendto focus on kinetochore microtubules, which clearly arestabilized in many systems (Inoue and Salmon, 1995). Sta-bilized microtubules also assemble in the midzone duringcytokinesis, presumably in response to decreasing Cdk1 ac-tivity and relocalization of Aurora-B to the midzone (Eggertet al., 2006), but there is no evidence for such a stabilizedmidzone population in metaphase.

Can we reconcile our findings with previous argumentsthat chromatin stabilizes microtubules in the egg extractsystem? In a recent experiment, the shape of asters wasmeasured near chromatin in TPX2-inhibited egg extracts,and these data were interpreted as predicting an approxi-mately three- to fourfold increase in the lifetime of microtu-bule with free plus ends in spindles (Athale et al., 2008). Ourdata clearly reject this degree of stabilization for the majorityof microtubules. In different experiments where dynamicswere not perturbed we observed best-fit � values that variedby �10%, which gives an approximate measure of the accu-racy of our method. Even halving the amount of MCAK didnot cause a three- to fourfold increase in stability. Addingconstitutively active Ran to X. laevis egg extracts promotesmicrotubule assembly (Carazo-Salas et al., 2001) and stabili-zation (Caudron et al., 2005). These data were interpreted asshowing that Ran-GTP causes microtubule stabilization nearchromatin in spindles, but other interpretations are possible.For example, Ran-GTP may promote nucleation but notstabilization, and/or it may selectively stabilize kinetochoremicrotubules. It is also possible that chromatin derived fac-tors act locally in spindles to destabilize microtubules, op-posing the stabilizing effects of the Ran-GTP and Aurora-Bgradients, and these influences were missed in observationsmade outside true spindles. For example, the dynamics ofmicrotubules in fully formed spindles—investigated here—might be substantially different from microtubule dynamicsduring the initial phases of spindle assembly, perhaps cor-responding to the stabilization suggested by Athale et al.(2008). Overall, our data strongly rejects the idea that allspindle microtubules are stabilized three- to fourfold nearchromatin in spindles. Our methods might fail to detect a

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Molecular Biology of the Cell330

small subset of microtubules that were selectively stabilized,if this population was �1% of the total, but we see noevidence of a longer lived tail in any of our lifetime distri-butions. We cannot rigorously rule out the existence of astructurally or biochemically differentiated, more stable,small subset of nonkinetochore microtubules, but we knowof no data that support the existence of such a subset. Aspecial subset of more stable microtubules, called the mid-zone array, does assemble near the cell equator during cy-tokinesis (discussed above), but there is no evidence that itexists during metaphase. It is possible that the pellicle-nu-cleated arrays we used to model the environment outsidespindles somehow induce microtubule stabilization. Argu-ing against a major effect of this kind, the kinetics of singlemicrotubule assembly from centrosomes in mitotic egg ex-tract (Belmont et al., 1990; Verde et al., 1992) is consistentwith the average microtubule lifetimes we infer in spindles.

Our data also speak strongly to the mechanism of rapidturnover of nonkinetochore microtubules in spindles thathas been mysterious since it was discovered by Inoue in the1950s (Inoue and Sato, 1967). Our lifetime distribution waswell fit by a model for first passage times of a biased randomwalk process, with an average lifetime of a microtubule ofaverage length of 16 s. This fit is consistent with turnoveroccurring by a rapid, stochastic process at microtubule ends,most likely dynamic instability of free plus ends. We cannotrule out a contribution from some kind of stochastic dynam-ics at minus ends, or slow depolymerization from minusends that makes little contribution to the lifetime distribu-tion. Our data do argue strongly against a treadmillingmodel for turnover (Margolis et al., 1978), because this classof model is expected to show a peak in the lifetime distri-bution, corresponding to the average length of time it takesa subunit incorporated at one end of the microtubules to belost at the other. Also, the lack of effect on turnover rate ofblocking microtubule sliding with FCPT shows that micro-tubule turnover and movement are mechanistically distinctprocesses. This argues strongly against feeder-chipper mod-els for turnover, because these require translocation of mi-crotubules into static depolymerase sites (Gadde and Heald,2004).

The biased random walk model is a phenomenologicalmodel that can quantitatively account for our lifetime dataand provides a convenient means of parameterizing thesedata. Evaluating the validity of more detailed, microscopicmodels of microtubule dynamics will require additionaldata that this simple model cannot explain. Another widelyused simple model of microtubule dynamics is the two-statemodel (Verde et al., 1992; Dogterom and Leibler, 1993), inwhich microtubules are taken to stochastically switch be-tween phases of constant polymerization and constant de-polymerization. These simple models ignore many featuresknown to be present in real microtubules, such as nanoscalefluctuations (Schek et al., 2007) and complex structural tran-sitions at the polymer ends (Anrnal et al., 2000). The two-state model predicts an exponential distribution of tubulinlifetimes in the absence of rescues (transitions from shrink-ing to growing; Bicout, 1997). Our measured lifetime distri-butions are clearly nonexponential, but it is possible thatthe large turnover at short times is caused by fluctuations ofthe tubulin-GTP cap (Howard and Hyman, 2009), whereasthe turnover at longer times is dominated by the lengthchanges of the microtubule. Although it would surely bepossible to construct models of microtubule dynamics ofthat nature that are consistent with our measured lifetimedistribution, because our data can already be accounted forby an even simpler model, we believe that it is more judi-

cious to wait for additional data that demonstrate the defi-ciencies of the biased random walk model. As an additionalprecaution, we separately analyzed the lifetime data fortimes �30 s, which can be well fit to a single exponential,and all of the conclusion obtained from analyzing the fulldata set hold equally well when only this restrict subset isconsidered.

Our interpretation makes testable predictions about theaverage length and length distribution of spindle microtu-bules that are largely independent of the details of plus-enddynamics. If the spindle does not cause stabilization as weassert, nonkinetochore microtubules in spindles should havethe same length distribution as microtubules grown fromcentrosomes in egg extracts, which is approximately expo-nential, with an average length of �3 �m (Verde et al., 1992).This proposed length distribution differs from publishedestimates using other methods. Correlated motions of indi-vidual tubulin molecules were used to infer a mean length of�20 �m and a bell-shaped distribution (Yang et al., 2007),but cross-linking might give rise to correlated motions oftubulin molecules in different microtubules, potentiallycomplicating this analysis. A different length estimate basedon measuring tubulin incorporation inferred an averagelength of �14 �m (Burbank et al., 2006). However, thistechnique used a number of unproven assumptions, such asthe hypothesis that a microtubule’s orientations can be de-finitively determined from its direction of motion, so theresulting estimate may be faulty. All of the current estimatesof microtubule lengths in X. laevis egg extract spindles areindirect, including our own, and direct measurements byelectron microscopy will be necessary to unambiguouslyresolve this issue.

If the locally high concentration of microtubules in spin-dles is not caused by local stabilization, what does cause it?We postulate it is solely due to an increased rate of nucle-ation in the spindle compared with bulk cytoplasm, andfurthermore, that understanding how nucleation is spatiallyregulated will be the key to understanding morphogenesisof meiotic spindles. Given that microtubule turnover is fastrelative to transport, nucleation has to occur throughout thespindle, as proposed by others (Mahoney et al., 2006). Morespecifically, during the metaphase steady state the pattern ofnucleation must preserve local microtubule density and lo-cal microtubule polarity. Nucleation is globally controlledby the Ran pathway (Karsenti and Vernos, 2001), but it isstill unclear how this generates spindle structure and givesrise to a sharp boundary between the inside and outside ofthe spindle. Mechanisms in which pre-existing microtubuleslocally stimulate nucleation are a possibility (Clausen andRibbeck, 2007), as per the Arp2/3 complex for actin. Onecandidate mechanism might involve orientation of the �-tu-bulin complex on microtubules by the augmin complex(Goshima et al., 2008). It is also possible that nucleationoccurs with random orientation, and newborn microtubulesare rapidly reoriented by motor proteins. Measurements oftubulin turnover, such as those presented here and else-where in the literature, cannot be used to directly probemicrotubule nucleation because the majority of tubulin isincorporated into preexisting microtubules in the spindle.Hopefully, new experimental techniques will be developedto characterize the nature and spatial regulation of microtu-bule nucleation in spindles.

Finally, our observation that the tubulin lifetime distribu-tion in the complex environment of the spindle can be welldescribed by a simple biased random walk model with asingle freely adjustable parameter is encouraging for effortsto provide a quantitative basis for cytoskeleton biology.

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Similar methods may be useful in investigating differentmicrotubule populations and the dynamics of other biolog-ical polymers.

ACKNOWLEDGMENTS

We thank the Woods Hole MBL Cell Division Group, especially Jay Gatlin, forhelpful discussions. We thank Alex Lobkvosky and Bulbul Chakraborty forinsightful conversations regarding models of dynamic instability. This workwas supported by National Institutes of Health grant GM-39565 (to T.J.M.)and a fellowship (to D.J.N.) from the Life Science Research Foundation,sponsored by Novartis.

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